%--------------------------------------------------------------------------
% computes the neutral stability curves associated with the 'frozen time'
% eigenvalue problem using a 'weighted' pseudoarclength continuation
% scheme. essentially, the Marangoni number is premultiplied by delta^2 in
% order to make it the same order of magnitude as the wavenumbers. this
% just increases the efficiency of the method.
%--------------------------------------------------------------------------


function [k, M] = lo_numeric_stab_curves

k = linspace(0, 3, 100);

fun = @(k, M) lo_comp_eigs(k, M);

M(1) = 80;

for i = 2:100
    
    M(i) = fzero(@(x) fun(k(i), x), M(i-1));
    
end


plot(k, M);